Checkered material ends up stretching despite seemingly proper UV unwrapping
The Checker texture is actually 3D - it divides the texture space into cubes.

There are actually 2 things going on here:

Your tree is missing the nodes illustrated below:



First thing:

In Blender, a procedural texture-space will default to 'Generated' if texture coordinates are not explicitly provided. Generated space is measured (0-1, min->max) along the sides of an object's bounding box. 

As  @3fingeredfrog has commented, the rotation of your mesh is not aligned with its object's axes, as you can see from the bounding box. So the mesh is at an angle to the Generated texture space. CtrlA  > applying rotation with the mesh aligned to the world would fix that.

Second thing:

(As @lemon has commented) Without the mapping nodes, the texture is not using your UV map; it's having no influence. If you do use the UV map, then a 2D slice at Z=0 (W=0)is taken out of the Checker texture,  mapped  0-1 in U and V. The shading points in your object look up the texture from that space, using the UV map you've provided, with the result shown in the picture.